Synchronisation and topology identification of stochastic delayed multi-group models with multi-dispersal and Markovian switching

Abstract

This paper is concerned with the synchronisation and topology identification of stochastic delayed multi-group models with multi-dispersal and Markovian switching (SDMM). Our model is characterised by a combination of the stochastic perturbation, multi-dispersal and Markovian switching, which can reasonably model the actual system. By utilising the graph theory, Lyapunov method and stochastically finite-time attractiveness, two sufficient criteria are obtained to ensure the topology identification of SDMM and finite-time topology identification of SDMM based on adaptive synchronisation and finite-time synchronisation, respectively. These criteria are closely related to the topology property of the network and can be easily verified in practice. Finally, two numerical examples are given to show the effectiveness of the main results.